Markovian Learning Processes

Abstract

Real-valued Markov processes with steps of the form $\Delta X_n = \theta _i (\lambda _i - X_n )$ or $\Delta X_n = \delta _i $, $i = 1, \cdots ,v$, arise frequently in the theory of human and animal learning. This paper first surveys results pertaining to the asymptotic behavior of such processes as $n \to \infty $. Next, general theorems are given that cover limiting behavior as $n \to \infty $ and, simultaneously, $\theta _i \to 0$ or $\delta _i \to 0$. Finally, an example of a two-dimensional learning process $X_n$ is presented.